1. Field of the Invention
The present invention relates to a method for facilitating recognition of objects by means of a discriminant analysis technique.
2. Description of the Prior Art
Most exploration wells that are drilled in underground formations are not systematically cored since the cost of a coring operation is very high, along with the constraints induced from the drilling operation. For example, in the particular case of log analysis, the method according to the invention allows recognition of the rock at the levels that are not cored. This is an important technical problem because little direct information on the nature of the rocks is generally available. On the other hand, logging measurements are systematically recorded from the moment that a hole is drilled. An abundant source of indirect data on the nature of the geologic formations is thus available, which is essential in order to deduce therefrom the geologic characteristics of the formations encountered while drilling. Logging measurements contain errors linked with the precision of the measuring system and with the recording quality. Thus, if the wall of the borehole is damaged, coupling of the measuring system with the formations will be defective and the measurements will be less reliable. It is important to involve the measuring quality in the determination of the type of the rock in order to better evaluate the reliability of the database which is formed after interpretation of the logs.
The recognition of seismic facies in a reservoir by analysis of the various seismic attributes recorded is a problem. This is also a very important problem because seismic measurements are the only source of information available, which covers all of the reservoir, unlike well measurements that are few and localized.
Various aspects of the prior art are described for example in the following reference documents:                Alefeld G. and Herzberger J., 1983, Introduction to Interval Computations; Computer Science and Applied Mathematics No.42, Academic Press, New York;        Dequirez P.-Y., Fournier F., Feuchtwanger T., Torriero D., 1995, Integrated Stratigraphic and Lithologic Interpretation of the East-Senlac Heavy Oil Pool; SEG, 65th Annual International Society of Exploration Geophysicists Meeting, Houston, Oct. 8-13 1995, Expanded Abstracts, CH1.4, pp. 104-107;        Epanechnikov V. A., 1969, Nonparametric Estimate of a Multivariate Probability Density; Theor. Probab. Appl., vol. 14, p. 179-188;        Hand D. J., 1981, Discrimination and Classification; Wiley Series in Probabilities and Mathematical Statistics, John Wiley & Sons, Chichester;        Jaulin L., 2000, Le Calcul Ensembliste par Analyse par Intervalles et Ses Applications; Mémoire d'Habilitation à Diriger des Recherches;        Kolmogorov A. N., 1950, Foundation of the Theory of Probability; Chelsea Publ. Co., New York;        Luenberger D. G., 1969, Optimization by Vector Space Methods; Series in Decision and Control, John Wiley & Sons, Chichester;        Moore R. E., 1969, Interval Analysis; Prenctice-Hall, Englewood Cliffs;        Pavec R., 1995, Some Algorithms Providing Rigourous Bounds for the Eigenvalues of a Matrix; Journal of Universal Computer Science, vol. 1 No.7, p. 548-559;        Walley P., 1991, Statistical Reasoning with Imprecise Probabilities; Monographs on Statistics and Applied Probabilities No.42, Chapman and Hall, London.        
Discriminant analysis is a known technique for recognition of geologic objects in underground formations. The objects are defined by a set of data of a certain number of variables or characteristics. For example, from a set of logs, it may be desired to predict the type of rock or of lithofacies that will be encountered for each depth point of a well, with reference to a knowledge base. This type of base is formed by learning from configurations known through observations or prior measurements performed for example on core samples taken at various well depth levels through the formation, thus allowing connection of typical depth points to lithofacies or rock types existing in the well. An analysis method of this type is described in U.S. Pat. No. 6,052,651 filed by the assignee.
Another example is given by the supervised seismic facies analysis methodology described for example by Dequirez et al., 1995, mentioned above. Portions of seismic traces, or seismic samples, are characterized by a set of parameters referred to as seismic attributes, and these attributes are used to classify traces in categories having a geologic sense. A learning stage is carried out beforehand on typical seismic traces obtained in the vicinity of wells representative of the geologic categories to be recognized, from well surveys, for example, of wells producing gas in relation to wells producing oil, or wells where the reservoir is porous in relation to wells where the reservoir is compact, or wells where the reservoir is predominantly sandy, in relation to wells where the reservoir is predominantly salty, etc.
The discriminant analysis technique however has certain limits. In particular, it does not allow accounting for uncertainties about the values of the variables used to classify the objects. This is a problem since these uncertainties are real. The measurements, whether logging or seismic measurements, are imprecise. One of the causes for this imprecision is linked with the tools used to obtain and to process the measurements. Another cause is linked with the experimental conditions. Big measurement differences can be observed for example if the logging sonde is in front of a damaged well wall or of an invaded formation, etc.